Trainer Shug McGaughey says he’d like to run Orb in the Belmont as long as the colt is doing well.

‘‘The Belmont Stakes is on our radar screen,’’ McGaughey said Sunday after arriving back at Belmont Park and checking on his Derby winner, who was vanned back earlier in the day.

After a talk with Orb’s owners Ogden Mills ‘‘Dinny’’ Phipps and Stuart Janney III, McGaughey said, ‘‘We just all came to the conclusion that we should just watch Orb and see. I think everything is in good shape. We’d like to run.

‘‘But yesterday took a little bit out of him and he’s already run five times this year and it’s only the middle of May. I’d sure like to have him fresh for Saratoga and a Jim Dandy/Travers kind of a go.’’

A year ago, there was great anticipation for a Triple try after I’ll Have Another won the Derby and Preakness, but the colt was scratched the day before the Belmont because of a tendon injury.

The most recent of 20 rematches between classic winners in the Belmont was two years ago, with Derby winner Animal Kingdom and Preakness winner Shackleford hooking up — but 24-1 long shot Ruler On Ice pulled the upset.

Hours after Oxbow’s win at 15-1 odds gave Lukas his record 14th Triple Crown race win — and sixth Preakness — the trainer and his colt were on the road back to Churchill Downs.

If both show up for the 1½-mile Belmont, a formidable lineup of challengers could be waiting. Todd Pletcher has five possible starters: Derby runners Revolutionary (third), Overanalyze (11th), and Palace Malice (12th), as well as a pair of fillies in Dreaming of Julia and Unlimited Budget.

Other possibles include Derby runner-up Golden Soul and Mylute (fifth in the Derby, third in the Preakness).

McGaughey was disappointed he couldn’t follow his first Derby win with his first Preakness win, but said, ‘‘Winning the Derby was my lifetime dream and we won it. I would have loved to have won yesterday and taken it to the next level.’’

Lukas, meanwhile, won his first Triple Crown race since 2000, when Commendable won the Belmont. Since that win, Lukas was 0 for 31 in 22 Triple Crown races before Saturday.

‘‘I still enjoy doing this so much,’’ he said. ‘‘I don’t wake up every day anymore trying to prove I can train a racehorse. When you’re younger, you keep trying to prove yourself. I’m very comfortable with where I’m at.’’

Oxbow, ridden by Hall of Famer Gary Stevens, took the lead just after the start and led every step of the way.

The winning time of 1:57.54 was the slowest since 1961, when Carry Back won in 1:57.60. No matter, it gave Stevens his third Preakness win to go along with his three Derby and three Belmont wins.

‘‘I can’t say that we thought we were going to win,’’ the 50-year rider said, ‘‘but we knew we had a chance to win.’’